Plan teachers week schedule

output.txt

     Monday   Tuesday Wednesday  Thursday    Friday  Saturday
0      Mike     Katie       Ali      Mike     Katie       Ali
1      Mike      Mike      Mike      Mike      Mike      Mike
2     Katie      Mike      Mike     Katie      Mike       Ali
3      Mike     Katie     Katie      Mike     Katie       Ali
4     Katie     Katie      Mike     Katie     Katie     Katie
5     Katie       Ali     Katie     Katie       Ali
6       Ali       Ali       Ali       Ali       Ali
7       Ali      Mike     Katie       Ali      Mike
Runtime:        00:00:00.1063270
Backtracks:     125

Teachers.cs

namespace Csp
{
    using System;
    using System.Collections.Generic;
    using System.Linq;
    using Decider.Csp.BaseTypes;
    using Decider.Csp.Global;
    using Decider.Csp.Integer;

    public static class Program
    {
        public static void Main()
        {
            try
            {
                var teachers = new[] { "Mike", "Katie", "Ali" };
                var numberOfTeachers = teachers.Length;

                var hours = Enumerable.Range(0, 8).ToList();
                var dayNames = new[] { "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday" };

                var monday = new List<VariableInteger>();
                var tuesday = new List<VariableInteger>();
                var wednesday = new List<VariableInteger>();
                var thursday = new List<VariableInteger>();
                var friday = new List<VariableInteger>();
                var saturday = new List<VariableInteger>();

                foreach (var period in hours)
                {
                    monday.Add(new VariableInteger(string.Format("Monday {0}", period), 1, numberOfTeachers));
                    tuesday.Add(new VariableInteger(string.Format("Tuesday {0}", period), 1, numberOfTeachers));
                    wednesday.Add(new VariableInteger(string.Format("Wednesday {0}", period), 1, numberOfTeachers));
                    thursday.Add(new VariableInteger(string.Format("Thursday {0}", period), 1, numberOfTeachers));
                    friday.Add(new VariableInteger(string.Format("Friday {0}", period), 1, numberOfTeachers));

                    if (period < 5)
                    {
                        saturday.Add(new VariableInteger(string.Format("Saturday {0}", period), 1, numberOfTeachers));
                    }
                }

                var weekdays = new[] { monday, tuesday, wednesday, thursday, friday }.ToList();
                var days = new[] { monday, tuesday, wednesday, thursday, friday, saturday }.ToList();
                var week = days.SelectMany(x => x).ToList();

                var constraints = new List<IConstraint>();

                // No teacher teaches more than 3 hours per weekday
                foreach (var teacher in Enumerable.Range(1, numberOfTeachers))
                {
                    foreach (var day in weekdays)
                    {
                        constraints.Add(new ConstraintInteger(day.
                            Select(x => x == teacher).
                            Aggregate((x, y) => x + y) <= 3));
                    }
                }

                // No teacher teaches for more than two consecutive hours
                foreach (var day in days)
                {
                    for (var window = 0; window < day.Count - 2; ++window)
                    {
                        var threeHourWindow = day.Skip(window).Take(3).ToList();

                        var q1 = threeHourWindow[0] != threeHourWindow[1] |
                            threeHourWindow[0] != threeHourWindow[2] |
                            threeHourWindow[1] != threeHourWindow[2];
                        constraints.Add(new ConstraintInteger(q1));
                    }
                }

                // No teacher teaches more than 16 hours per week
                foreach (var teacher in Enumerable.Range(1, numberOfTeachers))
                {
                    IEnumerable<ExpressionInteger> innerIq = week.
                        Select(x => x == teacher);
                    ExpressionInteger iq = innerIq
                        .Aggregate((x, y) => x + y) <= 16;
                    var q2 = new ConstraintInteger(iq);
                    constraints.Add(q2);
                }

                // No teacher has more than 3 morning sessions (first session)
                // select the morning sessions
                for (int window = 0; window < days.Count - 2; window++)
                {
                    var threeMorningSessions = days.Skip(window).Take(3).Select(x => x.First()).ToList();
                    constraints.Add(new AllDifferentInteger(threeMorningSessions));
                }

                // No teacher has more than 3 evening sessions (last session)
                for (int window = 0; window < days.Count - 2; window++)
                {
                    var threeEveningSessions = days.Skip(window).Take(3).Select(x => x.Last()).ToList();
                    constraints.Add(new AllDifferentInteger(threeEveningSessions));
                }

                IState<int> state = new StateInteger(week, constraints);
                state.StartSearch(out StateOperationResult searchResult);

                Console.Write(' ');
                for (int i = 0; i < days.Count; i++)
                {
                    var day = days[i];
                    Console.Write("{0,10}", dayNames[i]);
                }

                Console.WriteLine();
                for (int hour = 0; hour < hours.Count; hour++)
                {
                    Console.Write(hour);
                    for (int i = 0; i < days.Count; i++)
                    {
                        if (days[i].Count > hour)
                        {
                            Console.Write("{0,10}", teachers[days[i][hour].Value - 1]);
                        }
                        else
                        {
                            Console.Write(new string(' ', 10));
                        }
                    }

                    Console.WriteLine();
                }

                Console.WriteLine("Runtime:\t{0}\nBacktracks:\t{1}\n", state.Runtime, state.Backtracks);
            }
            catch (Exception ex)
            {
                Console.WriteLine(ex);
            }
        }
    }
}